In many modern applications, there is a desire for concurrent multi-band transmitters that are capable of transmitting concurrent multi-band signals. As used herein, a concurrent multi-band signal is a signal that occupies multiple distinct frequency bands. More specifically, a concurrent multi-band signal contains frequency components occupying a different continuous bandwidth for each of multiple frequency bands. The concurrent multi-band signal contains no frequency components between adjacent frequency bands. One example of a concurrent multi-band signal is a concurrent dual-band signal. One exemplary application for concurrent multi-band signals that is of particular interest is a multi-standard cellular communications system. A base station in a multi-standard cellular communications system may be required to simultaneously, or concurrently, transmit multiple signals for multiple different cellular communications protocols or standards (i.e., transmit a multi-band signal). Similarly, in some scenarios, a base station in a Long Term Evolution (LTE) cellular communications protocol may be required to simultaneously transmit signals in separate frequency bands.
A concurrent multi-band transmitter includes a multi-band power amplifier that operates to amplify a concurrent multi-band signal to be transmitted to a desired power level. Like their single-band counterparts, multi-band power amplifiers are configured to achieve maximum efficiency, which results in poor linearity. For single-band transmitters, digital predistortion of a digital input signal of the single-band transmitter is typically used to predistort the digital input signal using an inverse model of the nonlinearity of the power amplifier to thereby compensate, or counter-act, the nonlinearity of the power amplifier. By doing so, an overall response of the single-band transmitter is linearized.
One issue with concurrent multi-band transmitters is that conventional single-band digital predistortion techniques cannot be used. Specifically, as an example, a concurrent dual-band transmitter exhibits three types of intermodulation products at the output of the concurrent dual-band transmitter, as illustrated in FIG. 1. The first type of intermodulation products consist of intermodulation products around each carrier frequency (ω1 and ω2) that are solely due to the intermodulation between signal elements within each band, which is similar to what is found in a single-band transmitter and is referred to as in-band intermodulation. The second type of intermodulation products consist of intermodulation products that appear in the same frequency range as the in-band intermodulation but are the result of intermodulation products between signal elements in both frequency bands (i.e., both the frequency band centered at ω1 and the frequency band centered at ω2). This second type of intermodulation products is referred to as cross-modulation. Lastly, the third type of intermodulation products consist of intermodulation products between the two signals in both frequency bands that are located at Δω away from the lower and upper carrier frequencies. This third type of intermodulation products is referred to as out-of-band intermodulation.
Typically, the out-of-band intermodulation can be removed via filtering at the output of the power amplifier and, as such, can be ignored. However, the issue with the concurrent dual-band transmitter is that conventional single-band digital predistortion techniques cannot practically be used to compensate for both in-band intermodulation and cross-modulation. Specifically, treating the digital input signals of the concurrent dual-band transmitter as a single-band digital input signal and using a single digital predistorter to compensate for both in-band intermodulation and cross-modulation requires observing a bandwidth at the output of the concurrent dual-band transmitter that is extremely wide. As a result, a required sampling rate for Analog-to-Digital (A/D) conversion and the digital circuitry is too high for a practical implementation. Conversely, using two separate signal-band predistorters to independently compensate for distortion in each frequency band is insufficient because this approach does not compensate for cross-modulation.
In order to address these issues, a Dual-Band Digital Predistortion technique (referred to as 2D-DPD) was proposed in Bassam S. et al., “2-D Digital Predistortion (2D-DPD) Architecture for Concurrent Dual-Band Transmitter,” IEEE Transactions on Microwave Theory and Technique, Vol. 59, No. 10, October 2011, pp. 2547-2553. The 2D-DPD technique relies on separate predistorters and separate adaptors for each band. In particular, the 2D-DPD technique uses the following baseband model for the separate predistorters:
                                          y            1                    ⁡                      (            n            )                          =                              ∑                          m              =              0                                      M              -              1                                ⁢                                    ∑                              k                =                0                                            N                -                1                                      ⁢                                          ∑                                  j                  =                  0                                k                            ⁢                                                c                                      k                    ,                    j                    ,                    m                                                        (                    1                    )                                                  ⁢                                                      x                    1                                    ⁡                                      (                                          n                      -                      m                                        )                                                  ⁢                                                                                                                        x                        1                                            ⁡                                              (                                                  n                          -                          m                                                )                                                                                                                      k                    -                    j                                                  ⁢                                                                                                                        x                        2                                            ⁡                                              (                                                  n                          -                          m                                                )                                                                                                  j                                                                                        (        1        )                                                      y            2                    ⁡                      (            n            )                          =                              ∑                          m              =              0                                      M              -              1                                ⁢                                    ∑                              k                =                0                                            N                -                1                                      ⁢                                          ∑                                  j                  =                  0                                k                            ⁢                                                c                                      k                    ,                    j                    ,                    m                                                        (                    2                    )                                                  ⁢                                                      x                    2                                    ⁡                                      (                                          n                      -                      m                                        )                                                  ⁢                                                                                                                        x                        2                                            ⁡                                              (                                                  n                          -                          m                                                )                                                                                                                      k                    -                    j                                                  ⁢                                                                                                                        x                        1                                            ⁡                                              (                                                  n                          -                          m                                                )                                                                                                  j                                                                                        (        2        )            where yi(n) is the predistorted output signal of the digital predistorter for band i (i=1, 2 for the concurrent dual-band transmitter), M represents a memory depth of the 2D-DPD baseband model, N is the nonlinear order of the 2D-DPD baseband model (i.e., an order of nonlinearity compensated for by the digital predistorters), ck,j,m(i) are complex valued predistortion coefficients for the digital predistorter for band i that are configured by a corresponding adaptor for band i, x1 is the digital input signal for the first band, and x2 is the input signal for the second band.
One issue with the 2D-DPD technique is that the 2D-DPD baseband model of Equations (1) and (2) requires a large number of predistortion coefficients ck,j,m(i) to be adaptively configured by the corresponding adaptors. Specifically, since there are three summations, the number of predistortion coefficients ck,j,m(i) required by the 2D-DPD baseband model is M (K+1)(K+2). The large number of predistortion coefficients results in a high complexity, and thus high cost, DPD architecture.
In You-Jiang Liu et al., “Digital Predistortion for Concurrent Dual-Band Transmitters Using 2-D Modified Memory Polynomials,” IEEE Transactions on Microwave Theory and Techniques, Vol. 61, No. 1, January 2013, pp. 281-290 and You-Jiang Liu et al., “Low-complexity 2D behavioural model for concurrent dual-band power amplifiers,” Electronic Letters, Vol. 48, No. 11, May 2012, a 2D-Modified Memory Polynomial (2D-MMP) baseband model was proposed that reduces the number of predistortion coefficients. Like the 2D-DPD baseband model, the 2D-MMP baseband model relies on separate predistorters and separate adaptors for each frequency band. In particular, the 2D-MMP baseband model is defined as:
                                          y            1                    ⁡                      (            n            )                          =                              ∑                          m              =              0                                      M              -              1                                ⁢                                    ∑                              k                =                0                                            N                -                1                                      ⁢                                          c                                  k                  ,                  m                                                  (                  1                  )                                            ⁢                                                x                  1                                ⁡                                  (                                      n                    -                    m                                    )                                            ⁢                                                                                                                                    x                        1                                            ⁡                                              (                                                  n                          -                          m                                                )                                                              ⁢                                                                                                                  +                          j                                                ⁢                                                                                                  ⁢                                                  b                                                      k                            +                            1                                                                                (                            1                            )                                                                                                                                      ⁢                                                                  x                        2                                            ⁡                                              (                                                  n                          -                          m                                                )                                                                                                              k                                                                        (        3        )                                                      y            2                    ⁡                      (            n            )                          =                              ∑                          m              =              0                                      M              -              1                                ⁢                                    ∑                              k                =                0                                            N                -                1                                      ⁢                                          c                                  k                  ,                  m                                                  (                  2                  )                                            ⁢                                                x                  2                                ⁡                                  (                                      n                    -                    m                                    )                                            ⁢                                                                                                                                    x                        2                                            ⁡                                              (                                                  n                          -                          m                                                )                                                              ⁢                                                                                                                  +                          j                                                ⁢                                                                                                  ⁢                                                  b                                                      k                            +                            1                                                                                (                            2                            )                                                                                                                                      ⁢                                                                  x                        1                                            ⁡                                              (                                                  n                          -                          m                                                )                                                                                                              k                                                                        (        4        )            where bk+1(i) pre-calculated (k+1)-th order envelope coupling factors between x1 and x2.
While the 2D-MMP baseband model results in a reduction in the number of predistortion coefficients, a baseband model for dual-band, or more generally multi-band, digital predistortion having a further reduction in the number of predistortion coefficients and thus complexity is desired.